Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Friday 26 June 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 157,722 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 2[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bed… 27 mk454hr East of E…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bla… 9 bb12fd North West
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bro… 11 br33ql London
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_can… 9 ws111jp Midlands
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_cit… 12 n15lz London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_enf… 7 en40dy London
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ham… 6 dl62uu North Eas…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_har… 24 ts232la North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_kin… 6 kt11eu London
## [90m# … with 157,712 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 62
## 33 2020-04-02 East of England 64
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 92
## 43 2020-04-12 East of England 101
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 45
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 36
## 67 2020-05-06 East of England 31
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 33
## 70 2020-05-09 East of England 29
## 71 2020-05-10 East of England 22
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 26
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 25
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
## 83 2020-05-22 East of England 13
## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 17
## 86 2020-05-25 East of England 25
## 87 2020-05-26 East of England 14
## 88 2020-05-27 East of England 12
## 89 2020-05-28 East of England 17
## 90 2020-05-29 East of England 16
## 91 2020-05-30 East of England 9
## 92 2020-05-31 East of England 8
## 93 2020-06-01 East of England 17
## 94 2020-06-02 East of England 14
## 95 2020-06-03 East of England 10
## 96 2020-06-04 East of England 7
## 97 2020-06-05 East of England 12
## 98 2020-06-06 East of England 5
## 99 2020-06-07 East of England 9
## 100 2020-06-08 East of England 5
## 101 2020-06-09 East of England 6
## 102 2020-06-10 East of England 8
## 103 2020-06-11 East of England 0
## 104 2020-06-12 East of England 9
## 105 2020-06-13 East of England 5
## 106 2020-06-14 East of England 4
## 107 2020-06-15 East of England 7
## 108 2020-06-16 East of England 3
## 109 2020-06-17 East of England 7
## 110 2020-06-18 East of England 4
## 111 2020-06-19 East of England 7
## 112 2020-06-20 East of England 2
## 113 2020-06-21 East of England 3
## 114 2020-06-22 East of England 5
## 115 2020-06-23 East of England 4
## 116 2020-06-24 East of England 1
## 117 2020-03-01 London 0
## 118 2020-03-02 London 0
## 119 2020-03-03 London 0
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## 134 2020-03-18 London 27
## 135 2020-03-19 London 25
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## 137 2020-03-21 London 49
## 138 2020-03-22 London 54
## 139 2020-03-23 London 63
## 140 2020-03-24 London 87
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## 142 2020-03-26 London 129
## 143 2020-03-27 London 130
## 144 2020-03-28 London 122
## 145 2020-03-29 London 146
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## 147 2020-03-31 London 181
## 148 2020-04-01 London 202
## 149 2020-04-02 London 191
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## 170 2020-04-23 London 77
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## 172 2020-04-25 London 58
## 173 2020-04-26 London 53
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## 175 2020-04-28 London 43
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## 223 2020-06-15 London 1
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## 229 2020-06-21 London 3
## 230 2020-06-22 London 2
## 231 2020-06-23 London 0
## 232 2020-06-24 London 0
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## 234 2020-03-02 Midlands 0
## 235 2020-03-03 Midlands 1
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## 241 2020-03-09 Midlands 1
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## 243 2020-03-11 Midlands 2
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## 245 2020-03-13 Midlands 5
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## 247 2020-03-15 Midlands 5
## 248 2020-03-16 Midlands 11
## 249 2020-03-17 Midlands 8
## 250 2020-03-18 Midlands 13
## 251 2020-03-19 Midlands 8
## 252 2020-03-20 Midlands 28
## 253 2020-03-21 Midlands 13
## 254 2020-03-22 Midlands 31
## 255 2020-03-23 Midlands 33
## 256 2020-03-24 Midlands 41
## 257 2020-03-25 Midlands 48
## 258 2020-03-26 Midlands 64
## 259 2020-03-27 Midlands 72
## 260 2020-03-28 Midlands 89
## 261 2020-03-29 Midlands 92
## 262 2020-03-30 Midlands 90
## 263 2020-03-31 Midlands 123
## 264 2020-04-01 Midlands 140
## 265 2020-04-02 Midlands 142
## 266 2020-04-03 Midlands 124
## 267 2020-04-04 Midlands 151
## 268 2020-04-05 Midlands 164
## 269 2020-04-06 Midlands 140
## 270 2020-04-07 Midlands 123
## 271 2020-04-08 Midlands 186
## 272 2020-04-09 Midlands 139
## 273 2020-04-10 Midlands 127
## 274 2020-04-11 Midlands 142
## 275 2020-04-12 Midlands 139
## 276 2020-04-13 Midlands 120
## 277 2020-04-14 Midlands 116
## 278 2020-04-15 Midlands 147
## 279 2020-04-16 Midlands 102
## 280 2020-04-17 Midlands 118
## 281 2020-04-18 Midlands 115
## 282 2020-04-19 Midlands 92
## 283 2020-04-20 Midlands 107
## 284 2020-04-21 Midlands 86
## 285 2020-04-22 Midlands 78
## 286 2020-04-23 Midlands 103
## 287 2020-04-24 Midlands 79
## 288 2020-04-25 Midlands 72
## 289 2020-04-26 Midlands 81
## 290 2020-04-27 Midlands 74
## 291 2020-04-28 Midlands 68
## 292 2020-04-29 Midlands 53
## 293 2020-04-30 Midlands 56
## 294 2020-05-01 Midlands 64
## 295 2020-05-02 Midlands 51
## 296 2020-05-03 Midlands 52
## 297 2020-05-04 Midlands 61
## 298 2020-05-05 Midlands 58
## 299 2020-05-06 Midlands 59
## 300 2020-05-07 Midlands 48
## 301 2020-05-08 Midlands 34
## 302 2020-05-09 Midlands 37
## 303 2020-05-10 Midlands 42
## 304 2020-05-11 Midlands 33
## 305 2020-05-12 Midlands 45
## 306 2020-05-13 Midlands 40
## 307 2020-05-14 Midlands 37
## 308 2020-05-15 Midlands 40
## 309 2020-05-16 Midlands 34
## 310 2020-05-17 Midlands 31
## 311 2020-05-18 Midlands 34
## 312 2020-05-19 Midlands 34
## 313 2020-05-20 Midlands 36
## 314 2020-05-21 Midlands 32
## 315 2020-05-22 Midlands 27
## 316 2020-05-23 Midlands 34
## 317 2020-05-24 Midlands 19
## 318 2020-05-25 Midlands 26
## 319 2020-05-26 Midlands 33
## 320 2020-05-27 Midlands 29
## 321 2020-05-28 Midlands 27
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## 323 2020-05-30 Midlands 20
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## 342 2020-06-18 Midlands 14
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## 344 2020-06-20 Midlands 13
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## 347 2020-06-23 Midlands 10
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## 351 2020-03-03 North East and Yorkshire 0
## 352 2020-03-04 North East and Yorkshire 0
## 353 2020-03-05 North East and Yorkshire 0
## 354 2020-03-06 North East and Yorkshire 0
## 355 2020-03-07 North East and Yorkshire 0
## 356 2020-03-08 North East and Yorkshire 0
## 357 2020-03-09 North East and Yorkshire 0
## 358 2020-03-10 North East and Yorkshire 0
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## 361 2020-03-13 North East and Yorkshire 0
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## 363 2020-03-15 North East and Yorkshire 2
## 364 2020-03-16 North East and Yorkshire 3
## 365 2020-03-17 North East and Yorkshire 1
## 366 2020-03-18 North East and Yorkshire 2
## 367 2020-03-19 North East and Yorkshire 6
## 368 2020-03-20 North East and Yorkshire 5
## 369 2020-03-21 North East and Yorkshire 6
## 370 2020-03-22 North East and Yorkshire 7
## 371 2020-03-23 North East and Yorkshire 9
## 372 2020-03-24 North East and Yorkshire 8
## 373 2020-03-25 North East and Yorkshire 18
## 374 2020-03-26 North East and Yorkshire 21
## 375 2020-03-27 North East and Yorkshire 28
## 376 2020-03-28 North East and Yorkshire 35
## 377 2020-03-29 North East and Yorkshire 38
## 378 2020-03-30 North East and Yorkshire 64
## 379 2020-03-31 North East and Yorkshire 60
## 380 2020-04-01 North East and Yorkshire 67
## 381 2020-04-02 North East and Yorkshire 74
## 382 2020-04-03 North East and Yorkshire 100
## 383 2020-04-04 North East and Yorkshire 105
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## 385 2020-04-06 North East and Yorkshire 96
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## 387 2020-04-08 North East and Yorkshire 107
## 388 2020-04-09 North East and Yorkshire 111
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## 401 2020-04-22 North East and Yorkshire 84
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## 405 2020-04-26 North East and Yorkshire 65
## 406 2020-04-27 North East and Yorkshire 65
## 407 2020-04-28 North East and Yorkshire 57
## 408 2020-04-29 North East and Yorkshire 69
## 409 2020-04-30 North East and Yorkshire 57
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## 411 2020-05-02 North East and Yorkshire 48
## 412 2020-05-03 North East and Yorkshire 40
## 413 2020-05-04 North East and Yorkshire 49
## 414 2020-05-05 North East and Yorkshire 40
## 415 2020-05-06 North East and Yorkshire 51
## 416 2020-05-07 North East and Yorkshire 45
## 417 2020-05-08 North East and Yorkshire 42
## 418 2020-05-09 North East and Yorkshire 44
## 419 2020-05-10 North East and Yorkshire 40
## 420 2020-05-11 North East and Yorkshire 29
## 421 2020-05-12 North East and Yorkshire 27
## 422 2020-05-13 North East and Yorkshire 28
## 423 2020-05-14 North East and Yorkshire 31
## 424 2020-05-15 North East and Yorkshire 32
## 425 2020-05-16 North East and Yorkshire 35
## 426 2020-05-17 North East and Yorkshire 26
## 427 2020-05-18 North East and Yorkshire 30
## 428 2020-05-19 North East and Yorkshire 27
## 429 2020-05-20 North East and Yorkshire 22
## 430 2020-05-21 North East and Yorkshire 33
## 431 2020-05-22 North East and Yorkshire 22
## 432 2020-05-23 North East and Yorkshire 18
## 433 2020-05-24 North East and Yorkshire 26
## 434 2020-05-25 North East and Yorkshire 21
## 435 2020-05-26 North East and Yorkshire 21
## 436 2020-05-27 North East and Yorkshire 22
## 437 2020-05-28 North East and Yorkshire 20
## 438 2020-05-29 North East and Yorkshire 25
## 439 2020-05-30 North East and Yorkshire 20
## 440 2020-05-31 North East and Yorkshire 20
## 441 2020-06-01 North East and Yorkshire 16
## 442 2020-06-02 North East and Yorkshire 23
## 443 2020-06-03 North East and Yorkshire 22
## 444 2020-06-04 North East and Yorkshire 17
## 445 2020-06-05 North East and Yorkshire 17
## 446 2020-06-06 North East and Yorkshire 21
## 447 2020-06-07 North East and Yorkshire 14
## 448 2020-06-08 North East and Yorkshire 11
## 449 2020-06-09 North East and Yorkshire 11
## 450 2020-06-10 North East and Yorkshire 18
## 451 2020-06-11 North East and Yorkshire 7
## 452 2020-06-12 North East and Yorkshire 9
## 453 2020-06-13 North East and Yorkshire 10
## 454 2020-06-14 North East and Yorkshire 11
## 455 2020-06-15 North East and Yorkshire 8
## 456 2020-06-16 North East and Yorkshire 10
## 457 2020-06-17 North East and Yorkshire 8
## 458 2020-06-18 North East and Yorkshire 10
## 459 2020-06-19 North East and Yorkshire 6
## 460 2020-06-20 North East and Yorkshire 4
## 461 2020-06-21 North East and Yorkshire 4
## 462 2020-06-22 North East and Yorkshire 6
## 463 2020-06-23 North East and Yorkshire 5
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## 491 2020-03-27 North West 35
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## 530 2020-05-05 North West 48
## 531 2020-05-06 North West 44
## 532 2020-05-07 North West 49
## 533 2020-05-08 North West 42
## 534 2020-05-09 North West 30
## 535 2020-05-10 North West 41
## 536 2020-05-11 North West 35
## 537 2020-05-12 North West 38
## 538 2020-05-13 North West 25
## 539 2020-05-14 North West 26
## 540 2020-05-15 North West 33
## 541 2020-05-16 North West 32
## 542 2020-05-17 North West 24
## 543 2020-05-18 North West 31
## 544 2020-05-19 North West 35
## 545 2020-05-20 North West 27
## 546 2020-05-21 North West 26
## 547 2020-05-22 North West 26
## 548 2020-05-23 North West 31
## 549 2020-05-24 North West 26
## 550 2020-05-25 North West 31
## 551 2020-05-26 North West 27
## 552 2020-05-27 North West 27
## 553 2020-05-28 North West 28
## 554 2020-05-29 North West 20
## 555 2020-05-30 North West 19
## 556 2020-05-31 North West 13
## 557 2020-06-01 North West 12
## 558 2020-06-02 North West 27
## 559 2020-06-03 North West 22
## 560 2020-06-04 North West 22
## 561 2020-06-05 North West 15
## 562 2020-06-06 North West 23
## 563 2020-06-07 North West 19
## 564 2020-06-08 North West 20
## 565 2020-06-09 North West 15
## 566 2020-06-10 North West 14
## 567 2020-06-11 North West 16
## 568 2020-06-12 North West 8
## 569 2020-06-13 North West 8
## 570 2020-06-14 North West 15
## 571 2020-06-15 North West 15
## 572 2020-06-16 North West 11
## 573 2020-06-17 North West 10
## 574 2020-06-18 North West 11
## 575 2020-06-19 North West 7
## 576 2020-06-20 North West 11
## 577 2020-06-21 North West 6
## 578 2020-06-22 North West 10
## 579 2020-06-23 North West 8
## 580 2020-06-24 North West 4
## 581 2020-03-01 South East 0
## 582 2020-03-02 South East 0
## 583 2020-03-03 South East 1
## 584 2020-03-04 South East 0
## 585 2020-03-05 South East 1
## 586 2020-03-06 South East 0
## 587 2020-03-07 South East 0
## 588 2020-03-08 South East 1
## 589 2020-03-09 South East 1
## 590 2020-03-10 South East 1
## 591 2020-03-11 South East 1
## 592 2020-03-12 South East 0
## 593 2020-03-13 South East 1
## 594 2020-03-14 South East 1
## 595 2020-03-15 South East 5
## 596 2020-03-16 South East 8
## 597 2020-03-17 South East 7
## 598 2020-03-18 South East 10
## 599 2020-03-19 South East 9
## 600 2020-03-20 South East 13
## 601 2020-03-21 South East 7
## 602 2020-03-22 South East 25
## 603 2020-03-23 South East 20
## 604 2020-03-24 South East 22
## 605 2020-03-25 South East 29
## 606 2020-03-26 South East 35
## 607 2020-03-27 South East 34
## 608 2020-03-28 South East 36
## 609 2020-03-29 South East 55
## 610 2020-03-30 South East 58
## 611 2020-03-31 South East 65
## 612 2020-04-01 South East 66
## 613 2020-04-02 South East 55
## 614 2020-04-03 South East 72
## 615 2020-04-04 South East 80
## 616 2020-04-05 South East 82
## 617 2020-04-06 South East 88
## 618 2020-04-07 South East 100
## 619 2020-04-08 South East 83
## 620 2020-04-09 South East 104
## 621 2020-04-10 South East 88
## 622 2020-04-11 South East 88
## 623 2020-04-12 South East 88
## 624 2020-04-13 South East 84
## 625 2020-04-14 South East 65
## 626 2020-04-15 South East 72
## 627 2020-04-16 South East 56
## 628 2020-04-17 South East 86
## 629 2020-04-18 South East 57
## 630 2020-04-19 South East 70
## 631 2020-04-20 South East 87
## 632 2020-04-21 South East 50
## 633 2020-04-22 South East 54
## 634 2020-04-23 South East 57
## 635 2020-04-24 South East 64
## 636 2020-04-25 South East 51
## 637 2020-04-26 South East 51
## 638 2020-04-27 South East 40
## 639 2020-04-28 South East 40
## 640 2020-04-29 South East 47
## 641 2020-04-30 South East 29
## 642 2020-05-01 South East 37
## 643 2020-05-02 South East 36
## 644 2020-05-03 South East 17
## 645 2020-05-04 South East 35
## 646 2020-05-05 South East 29
## 647 2020-05-06 South East 25
## 648 2020-05-07 South East 27
## 649 2020-05-08 South East 26
## 650 2020-05-09 South East 28
## 651 2020-05-10 South East 19
## 652 2020-05-11 South East 25
## 653 2020-05-12 South East 27
## 654 2020-05-13 South East 18
## 655 2020-05-14 South East 32
## 656 2020-05-15 South East 24
## 657 2020-05-16 South East 22
## 658 2020-05-17 South East 18
## 659 2020-05-18 South East 22
## 660 2020-05-19 South East 12
## 661 2020-05-20 South East 22
## 662 2020-05-21 South East 15
## 663 2020-05-22 South East 17
## 664 2020-05-23 South East 21
## 665 2020-05-24 South East 17
## 666 2020-05-25 South East 13
## 667 2020-05-26 South East 19
## 668 2020-05-27 South East 18
## 669 2020-05-28 South East 12
## 670 2020-05-29 South East 21
## 671 2020-05-30 South East 8
## 672 2020-05-31 South East 10
## 673 2020-06-01 South East 11
## 674 2020-06-02 South East 13
## 675 2020-06-03 South East 17
## 676 2020-06-04 South East 11
## 677 2020-06-05 South East 11
## 678 2020-06-06 South East 10
## 679 2020-06-07 South East 11
## 680 2020-06-08 South East 7
## 681 2020-06-09 South East 10
## 682 2020-06-10 South East 10
## 683 2020-06-11 South East 5
## 684 2020-06-12 South East 5
## 685 2020-06-13 South East 4
## 686 2020-06-14 South East 6
## 687 2020-06-15 South East 7
## 688 2020-06-16 South East 10
## 689 2020-06-17 South East 8
## 690 2020-06-18 South East 4
## 691 2020-06-19 South East 6
## 692 2020-06-20 South East 4
## 693 2020-06-21 South East 3
## 694 2020-06-22 South East 2
## 695 2020-06-23 South East 2
## 696 2020-06-24 South East 0
## 697 2020-03-01 South West 0
## 698 2020-03-02 South West 0
## 699 2020-03-03 South West 0
## 700 2020-03-04 South West 0
## 701 2020-03-05 South West 0
## 702 2020-03-06 South West 0
## 703 2020-03-07 South West 0
## 704 2020-03-08 South West 0
## 705 2020-03-09 South West 0
## 706 2020-03-10 South West 0
## 707 2020-03-11 South West 1
## 708 2020-03-12 South West 0
## 709 2020-03-13 South West 0
## 710 2020-03-14 South West 1
## 711 2020-03-15 South West 0
## 712 2020-03-16 South West 0
## 713 2020-03-17 South West 2
## 714 2020-03-18 South West 2
## 715 2020-03-19 South West 4
## 716 2020-03-20 South West 3
## 717 2020-03-21 South West 6
## 718 2020-03-22 South West 7
## 719 2020-03-23 South West 8
## 720 2020-03-24 South West 7
## 721 2020-03-25 South West 9
## 722 2020-03-26 South West 11
## 723 2020-03-27 South West 13
## 724 2020-03-28 South West 21
## 725 2020-03-29 South West 18
## 726 2020-03-30 South West 23
## 727 2020-03-31 South West 23
## 728 2020-04-01 South West 22
## 729 2020-04-02 South West 23
## 730 2020-04-03 South West 30
## 731 2020-04-04 South West 42
## 732 2020-04-05 South West 32
## 733 2020-04-06 South West 34
## 734 2020-04-07 South West 39
## 735 2020-04-08 South West 47
## 736 2020-04-09 South West 24
## 737 2020-04-10 South West 46
## 738 2020-04-11 South West 43
## 739 2020-04-12 South West 23
## 740 2020-04-13 South West 27
## 741 2020-04-14 South West 24
## 742 2020-04-15 South West 32
## 743 2020-04-16 South West 29
## 744 2020-04-17 South West 33
## 745 2020-04-18 South West 25
## 746 2020-04-19 South West 31
## 747 2020-04-20 South West 26
## 748 2020-04-21 South West 26
## 749 2020-04-22 South West 23
## 750 2020-04-23 South West 17
## 751 2020-04-24 South West 19
## 752 2020-04-25 South West 15
## 753 2020-04-26 South West 27
## 754 2020-04-27 South West 13
## 755 2020-04-28 South West 17
## 756 2020-04-29 South West 15
## 757 2020-04-30 South West 26
## 758 2020-05-01 South West 6
## 759 2020-05-02 South West 7
## 760 2020-05-03 South West 10
## 761 2020-05-04 South West 17
## 762 2020-05-05 South West 14
## 763 2020-05-06 South West 19
## 764 2020-05-07 South West 16
## 765 2020-05-08 South West 6
## 766 2020-05-09 South West 11
## 767 2020-05-10 South West 5
## 768 2020-05-11 South West 8
## 769 2020-05-12 South West 7
## 770 2020-05-13 South West 7
## 771 2020-05-14 South West 6
## 772 2020-05-15 South West 4
## 773 2020-05-16 South West 4
## 774 2020-05-17 South West 6
## 775 2020-05-18 South West 4
## 776 2020-05-19 South West 6
## 777 2020-05-20 South West 1
## 778 2020-05-21 South West 9
## 779 2020-05-22 South West 6
## 780 2020-05-23 South West 6
## 781 2020-05-24 South West 3
## 782 2020-05-25 South West 8
## 783 2020-05-26 South West 11
## 784 2020-05-27 South West 5
## 785 2020-05-28 South West 10
## 786 2020-05-29 South West 7
## 787 2020-05-30 South West 3
## 788 2020-05-31 South West 2
## 789 2020-06-01 South West 7
## 790 2020-06-02 South West 2
## 791 2020-06-03 South West 5
## 792 2020-06-04 South West 2
## 793 2020-06-05 South West 2
## 794 2020-06-06 South West 1
## 795 2020-06-07 South West 3
## 796 2020-06-08 South West 3
## 797 2020-06-09 South West 0
## 798 2020-06-10 South West 0
## 799 2020-06-11 South West 2
## 800 2020-06-12 South West 2
## 801 2020-06-13 South West 2
## 802 2020-06-14 South West 0
## 803 2020-06-15 South West 1
## 804 2020-06-16 South West 1
## 805 2020-06-17 South West 0
## 806 2020-06-18 South West 0
## 807 2020-06-19 South West 0
## 808 2020-06-20 South West 2
## 809 2020-06-21 South West 0
## 810 2020-06-22 South West 1
## 811 2020-06-23 South West 0
## 812 2020-06-24 South West 01.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Thursday 25 Jun 2020.
1.6 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 10,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 8,
lab_pos_y = 30200,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
rotate_x +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -10.1993 -2.5629 -0.3803 3.4485 5.6660
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.875e+00 5.375e-02 90.70 <2e-16 ***
## note_lag 1.223e-05 5.454e-07 22.42 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 12.90006)
##
## Null deviance: 6906.98 on 54 degrees of freedom
## Residual deviance: 704.64 on 53 degrees of freedom
## (23 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 130.942881 1.000012
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 117.705519 145.313867
## note_lag 1.000011 1.000013
Rsq(lag_mod)
## [1] 0.8979809
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.3.0 lubridate_1.7.9
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.14
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.1.1
## [10] projections_0.5.0 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.0 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.0 tibble_3.0.1 ggplot2_3.3.2
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 selectr_0.4-2 ggsignif_0.6.0 ellipsis_0.3.1
## [5] rprojroot_1.3-2 snakecase_0.11.0 fs_1.4.1 rstudioapi_0.11
## [9] farver_2.0.3 fansi_0.4.1 splines_3.6.3 knitr_1.29
## [13] jsonlite_1.7.0 broom_0.5.6 dbplyr_1.4.4 compiler_3.6.3
## [17] httr_1.4.1 backports_1.1.8 assertthat_0.2.1 Matrix_1.2-18
## [21] cli_2.0.2 htmltools_0.5.0 prettyunits_1.1.1 tools_3.6.3
## [25] gtable_0.3.0 glue_1.4.1 Rcpp_1.0.4.6 carData_3.0-4
## [29] cellranger_1.1.0 vctrs_0.3.1 nlme_3.1-144 matchmaker_0.1.1
## [33] crosstalk_1.1.0.1 xfun_0.15 ps_1.3.3 openxlsx_4.1.5
## [37] lifecycle_0.2.0 rstatix_0.6.0 MASS_7.3-51.5 scales_1.1.1
## [41] hms_0.5.3 sodium_1.1 yaml_2.2.1 curl_4.3
## [45] gridExtra_2.3 stringi_1.4.6 kyotil_2019.11-22 boot_1.3-24
## [49] pkgbuild_1.0.8 zip_2.0.4 rlang_0.4.6 pkgconfig_2.0.3
## [53] evaluate_0.14 lattice_0.20-38 labeling_0.3 htmlwidgets_1.5.1
## [57] cowplot_1.0.0 processx_3.4.2 tidyselect_1.1.0 plyr_1.8.6
## [61] magrittr_1.5 R6_2.4.1 generics_0.0.2 DBI_1.1.0
## [65] pillar_1.4.4 haven_2.3.1 foreign_0.8-75 withr_2.2.0
## [69] mgcv_1.8-31 survival_3.1-8 abind_1.4-5 modelr_0.1.8
## [73] crayon_1.3.4 car_3.0-8 utf8_1.1.4 rmarkdown_2.3
## [77] viridis_0.5.1 grid_3.6.3 readxl_1.3.1 data.table_1.12.8
## [81] blob_1.2.1 callr_3.4.3 reprex_0.3.0 digest_0.6.25
## [85] webshot_0.5.2 munsell_0.5.0 viridisLite_0.3.0